|
%I #5 Oct 04 2017 18:39:49
%S 0,-1,0,1,2,0,-3,-5,-1,7,12,3,-16,-27,-7,37,64,20,-85,-152,-55,191,
%T 356,141,-436,-841,-364,991,1988,938,-2233,-4674,-2369,5044,11004,
%U 5963,-11361,-25898,-14959,25467,60821,37245,-56995,-142783,-92384,127136,334946,228385,-282392
%N G.f.: Im(1/(1 + i*x/(1 + i*x^2/(1 + i*x^3/(1 + i*x^4/(1 + i*x^5/(1 + ...))))))), a continued fraction, where i is the imaginary unit.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>
%F G.f.: Im( (Sum_{k>=0} i^k*x^(k*(k+1))/Product(m=1..k} (1 - x^m)) / (Sum_{k>=0} i^k*x^(k^2)/Product(m=1..k} (1 - x^m)) ), where i is the imaginary unit.
%e G.f. A(x) = Sum_{n>=0} (A293268(n) + i*a(n))*x^n = 1 - i*x - x^2 - (1 - i)*x^3 + (1 + 2*i)*x^4 + 3*x^5 + (2 - 3*i)*x^6 - (2 + 5*i)*x^7 - (7 + i)*x^8 - ...
%t nmax = 48; Im[CoefficientList[Series[1/(1 + ContinuedFractionK[I x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]]
%t nmax = 48; Im[CoefficientList[Series[Sum[I^k x^(k (k + 1)) / Product[1 - x^m, {m, 1, k}], {k, 0, nmax}] / Sum[I^k x^(k^2) / Product[1 - x^m, {m, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]]
%Y Cf. A007325, A278400, A292137, A293268.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Oct 04 2017
|
